john d. lewis and jeffrey l. elmanelman/papers/lewiselman-ds2008.pdf · matter (lewis &...

Developmental Science 11:1 (2008), pp 135–155 DOI: 10.1111/j.1467-7687.2007.00634.x

© 2007 The Authors. Journal compilation © 2007 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

Blackwell Publishing LtdPAPER

Growth-related neural reorganization and the autism phenotype: a test of the hypothesis that altered brain growth leads to altered connectivity

John D. Lewis and Jeffrey L. ElmanDepartment of Cognitive Science, University of California at San Diego, USA

Abstract

Theoretical considerations, and findings from computational modeling, comparative neuroanatomy and developmentalneuroscience, motivate the hypothesis that a deviant brain growth trajectory will lead to deviant patterns of change in cortico-cortical connectivity. Differences in brain size during development will alter the relative cost and effectiveness of short- andlong-distance connections, and should thus impact the growth and retention of connections. Reduced brain size should favorlong-distance connectivity; brain overgrowth should favor short-distance connectivity; and inconsistent deviations from thenormal growth trajectory – as occurs in autism – should result in potentially disruptive changes to established patterns offunctional and physical connectivity during development. To explore this hypothesis, neural networks which modeled inter-hemispheric interaction were grown at the rate of either typically developing children or children with autism. The influence ofthe length of the inter-hemispheric connections was analyzed at multiple developmental time-points. The networks that modeledautistic growth were less affected by removal of the inter-hemispheric connections than those that modeled normal growth –indicating a reduced reliance on long-distance connections – for short response times, and this difference increased substantiallyat approximately 24 simulated months of age. The performance of the networks showed a corresponding decline during develop-ment. And direct analysis of the connection weights showed a parallel reduction in connectivity. These modeling results supportthe hypothesis that the deviant growth trajectory in autism spectrum disorders may lead to a disruption of established patternsof functional connectivity during development, with potentially negative behavioral consequences, and a subsequent reductionin physical connectivity. The results are discussed in relation to the growing body of evidence of reduced functional and structuralconnectivity in autism, and in relation to the behavioral phenotype, particularly the developmental aspects.

Introduction

Brain size has been found to be strongly correlated withrelative long-distance cortico-cortical connectivity acrossspecies (Rilling & Insel, 1999; Zhang & Sejnowski, 2000),and also, though less strongly, within species (Jancke,Staiger, Schlaug, Huang & Steinmetz, 1997). Evidencethat such a relationship also holds developmentally(Jancke, Preis & Steinmetz, 1999; Lewis & Courchesne,2004; Lewis, Courchesne & Elman, 2003, 2004) suggestsa link between findings of deviant brain growth trajecto-ries in developmental disorders (Bailey, Luthbert, Dean,Harding, Janota, Montgomery, Rutter & Lantos, 1998; Bau-man & Kemper, 1985; Courchesne, Carper & Akshoomoff,2003; Courchesne, Karns, Davis, Ziccardi, Carper, Tigue,Chisum, Moses, Pierce, Lord, Lincoln, Pizzo, Schreib-man, Haas, Akshoomoff & Courchesne, 2001; Hagberg,Stenbom & Engerström, 2001; Hazlett, Poe, Gerig,Smith, Provenzale, Ross, Gilmore & Piven, 2005) andfindings of abnormalities in cortico-cortical connectivityin these disorders (Barnea-Goraly, Kwon, Menon, Eliez,

Lotspeich & Reiss, 2004; Baron-Cohen, Knickmeyer &Belmonte, 2005; Egaas, Courchesne & Saitoh, 1995;Lewis & Courchesne, 2004; Lewis, Courchesne & Elman,2003, 2004; Piven, Bailey, Ranson & Arndt, 1997; Vidal,Nicolson, DeVito, Hayashi, Geaga, Drost, Williamson,Rajakumer, Sul, Dutton, Toga & Thompson, 2006;Waiter, Williams, Murray, Gilchrist, Perrett & Whiten,2005) – and possibly between these findings and behavior(Belmonte, Allen, Beckel-Mitchener, Boulanger, Carper& Webb, 2004; Castelli, Frith, Happe & Frith, 2002;Deutsch & Joseph, 2003; Just, Cherkassky, Keller &Minshew, 2004; Pelphrey, Morris & McCarthy, 2005;Tager-Flusberg & Joseph, 2003). Brain size is inverselycorrelated with the ratio of inter-hemispheric white-matter to gray-matter (Jancke et al., 1999; Jancke et al.,1997; Rilling & Insel, 1999), and presumably with theratio of long-distance cortico-cortical connections, ingeneral, to gray-matter (Zhang & Sejnowski, 2000). Thusdevelopmental disorders in which brain size is abnormallysmall throughout development should show increasedlong-distance connectivity; and those in which brain size

Address for correspondence: John D. Lewis, Department of Cognitive Science, UC San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0515, USA;e-mail: [email protected]

136 John D. Lewis and Jeffrey L. Elman

© 2007 The Authors. Journal compilation © 2007 Blackwell Publishing Ltd.

is abnormally large should show decreased long-distanceconnectivity. In cases in which brain size abnormali-ties are not consistent throughout development, morecomplex and possibly more detrimental effects on con-nectivity might be expected.

The relation between brain size and connectivity hasbeen hypothesized to stem from the relations betweenbrain size and conduction delay and between brain sizeand the cellular costs associated with long-distanceconnections (Lewis & Courchesne, 2004; Lewis et al.,2003, 2004; Ringo, Doty, Demeter & Simard, 1994). Theconduction delay associated with either a myelinated oran unmyelinated axon is primarily a function of itsdiameter and length (Waxman, 1977); and differences inbrain size necessarily correlate with differences in thelengths of long-distance connections, but appear tocorrelate only weakly with differences in axon diameters(Olivares, Montiel & Aboitiz, 2001). Thus, differences inbrain size should alter the relative usefulness of short-and long-distance connections for tasks that require rapidresponses. The cell maintenance costs associated withlong-distance connections should also correlate with brainsize, and so differences in brain size should also alter therelative costs of short- and long-distance connections.

Both intra- and inter-hemispheric connectivity appearto be arrived at via prenatal exuberance followed bypostnatal pruning (LaMantia & Rakic, 1990; Rakic,Bourgeois, Eckenhoff, Zecevic & Goldman-Rakic, 1986),the latter of which is thought to be moderated by anactivity dependent competition for neurotrophins (Barres& Raff, 1993; Callaway, Soha & Van Essen, 1987; VanOoyen & Willshaw, 1999). Brain size differences duringdevelopment should impact this competition, and so thegrowth and retention of connections (Lewis & Courchesne,2004; Lewis et al., 2003, 2004). In abnormal develop-ment, in periods of time in which brain size is abnormallysmall, long-distance connections should be favored, andduring periods of time in which brain size is abnormallylarge, short-distance connections should be favored. Braindevelopment is not spatio-temporally homogeneous –evidence supports heterochronous development in typicallydeveloping children (Giedd, Blumenthal, Jeffries,Castellanos, Liu, Zijdenbos, Paus, Evans & Rapoport,1999; Thompson, Giedd, Woods, MacDonald, Evans &Toga, 2000) – and so the effects of brain size abnormalitieson connectivity should be expected to be temporally andspatially linked. A growth trajectory in which there is adevelopmentally inconsistent brain-size abnormalityshould thus show a corresponding fluctuation in thepattern of connectivity in spatial accord with the temporalaspects of the brain size abnormalities. And a very rapidchange in the growth trajectory might be expected toalter established patterns of connectivity within a givenbrain area – abandoning connections in which early learninghas been represented, potentially giving rise to abnor-malities in the behaviors that relied on those connections.

There is now consistent evidence from post mortemstudies (Bailey et al., 1998; Bauman & Kemper, 1985;

Kemper & Bauman, 1998), head circumference measures(Aylward, Minshew, Field, Sparks & Singh, 2002; Bailey,Luthert, Bolton, LeCouteur, Rutter & Harding, 1993;Courchesne et al., 2003; Davidovitch, Patterson &Gartside, 1996; Dementieva, Vance, Donnelly, Elston,Wolpert, Ravan, DeLong, Abramson, Wright & Cuccaro,2005; Fombonne, Roge, Claverie, County & Fremolle,1999; Hazlett et al., 2005; Lainhart, Piven, Wzorek,Landa, Santangelo, Coon & Folstein, 1997; Miles, Hadden,Takahashi & Hillman, 2000; Woodhouse, Bailey, Rutter,Bolton, Baird & Couteur, 1996) and MRI volumetricanalyses (Aylward et al., 2002; Courchesne et al., 2001;Piven, Arndt, Bailey, Havercamp, Andreason & Palmer,1995; Sparks, Friedman, Shaw, Aylward, Echelard,Artru, Maravilla, Giedd, Munson, Dawson & Dager,2002) that individuals with autism spectrum disordershave abnormally large brains after the second or thirdyear of life, and that, early in development, this sizedifference can be multiple standard deviations above thenorm (Courchesne et al., 2003; Courchesne et al., 2001;Dementieva et al., 2005; Hazlett et al., 2005; Sparkset al., 2002). Children later diagnosed with autismspectrum disorders, however, have head circumferencemeasures at birth that are normal (Hazlett et al., 2005;Hultman, Sparen & Cnattingius, 2002), or even slightlysmaller than normal (Courchesne et al., 2003; Redcay &Courchesne, 2005). That these results stem from acceler-ated growth over the first years of life is supported bylongitudinal data (Courchesne et al., 2003; Dementievaet al., 2005; Hazlett et al., 2005). Thus, autism appearsto be an example of a developmental disorder showingan abrupt increase in brain size after a period of normalor slightly reduced growth.

This pattern of growth is predicted to show disrup-tions in the initially established patterns of functionalconnectivity, abnormalities in the behaviors associatedwith these disruptions, and a subsequent reduction inphysical connectivity.

There is a growing body of evidence of reducedlarge-scale functional and structural connectivity inadults with autism spectrum disorders (Castelli et al.,2002; Egaas et al., 1995; Just et al., 2004; Kana, Keller,Cherkassky, Minshew & Just, 2006; Koshino, Carpenter,Minshew, Cherkassky, Keller & Just, 2005; Manes,Piven, Vrancic, Nanclares, Plebst & Starkstein, 1999;Piven et al., 1997; Ring, Baron-Cohen, Wheelwright,Williams, Brammer, Andrew & Bullmore, 1999; Vidal et al.,2006). And it has been proposed that the deficits inautism are a result of reduced integration of informationdue to this underconnectivity (Herbert, 2005; Just et al.,2004). But there are no studies of the developmentalchanges in functional connectivity; and the relationsbetween the trajectory of brain growth and the behavioralphenotype, and physical connectivity, are almostunknown. The growth of inter-hemispheric connectivityin children with autism spectrum disorders appears to beinversely related to brain size between 4 and 10 years ofage (Lewis & Courchesne, 2004; Lewis et al., 2004), and

Altered brain growth and autism 137


by late childhood or adolescence, individuals withautism spectrum disorders show abnormal increases ingray-matter (Waiter, Williams, Murray, Gilchrist, Perrett& Whiten, 2004), decreases in inter-hemispheric white-matter (Lewis & Courchesne, 2004; Lewis et al., 2004;Waiter et al., 2005), and increased short-distanceconnectivity (Herbert, Ziegler, Makris, Filipek, Kemper,Normandin, Sanders, Kennedy & Caviness, 2004). Andthere is also some indication that the degree of abnormalityin the rate of brain growth is related to the severity ofthe outcome (Akshoomoff, Lord, Lincoln, Courchesne,Carper, Townsend & Courchesne, 2004; Courchesneet al., 2003; Deutsch & Joseph, 2003; cf. Sparks et al.,2002; Tager-Flusberg & Joseph, 2003). But there isessentially no research that relates the shape of the braingrowth trajectory in the first years of life to developmentalchanges in functional connectivity, structural connectivity,or to the particular aspects of the behavioral phenotypethat might be vulnerable to reorganization.

This paper reports on a computational study of thepossibility of such effects of brain growth on develop-mental patterns of connectivity and performance.Neural networks ‘grown’ in accord with either thebrain-growth patterns of typically developing childrenor children with autism were used to explore thispossibility.

Methods

Architecture and training

The simple two-hemisphere model shown in Figure 1was used to explore this hypothesis. This architecturewas based on that used by Ringo et al. (1994). The net-work comprised two ‘hemispheres’ of 10 units each,five input units and five output units for each hemisphere,and a number of units used to implement conductiondelay in inter- and intra-hemispheric connections. Eachunit in both hemispheres was fully connected with thenine other units in that hemisphere, and all of these unitswere recurrent. Two units in each hemisphere also hadafferent and efferent connections with two units in theother hemisphere. The five input units for a hemispherewere fully connected with that hemisphere; and eachhemisphere was fully connected with five output units.

Both inter- and intra-hemispheric connections wereassociated with conduction delays, implemented byconstructing these connections as chains of copy units.The conduction delay was the number of links in aninter- or intra-hemispheric chain. The delay associatedwith an inter-hemispheric connection was a function ofage, based on the head circumference growth trajectoriesfor either typically developing children or children withautism. The delay function was:

DelayINTER(age, diagnosis) = * (HC(age, diagnosis)/π)/ConductionVelocity(age)

where HC(age, diagnosis) is the head circumference atthe given age for the given diagnosis, and Conduction-Velocity(age) is an increasing linear function of age.The inter-hemispheric delay was thus of the diameterof a spherical head corresponding to HC(age, diagnosis)– a crude approximation of the length of the inter-hemispheric connections taking scalp, skull, corticalthickness, and cortical folding into account – divided byConductionVelocity(age) – a crude approximation of theincreases in axon diameter and myelination that occurover development. The delay associated with an intra-hemispheric connection was identical for both the networksmodeling typical brain growth and the networks modelingautistic brain growth; it was of the inter-hemisphericdelay associated with the typical brain growth pattern.These functions are plotted in Figure 2. The develop-mental changes in the conduction delays associated withinter- and intra-hemispheric connections are, of course,a far more complex combination of non-linear functionswhich differ between regions; the connections may fol-low complex paths that are substantially greater than of the diameter of the head; and heads are not spherical.But these functions are plausibly an index of the actualaverage conduction delays associated with the two typesof connections.

The growth trajectory for networks modeling typicaldevelopment was based on head circumference measuresfrom standardized growth charts (Kuczmarski, Ogden,Guo et al., 2002; Nellhaus, 1968) and on prenatal measurestaken by ultrasound (Kurmanavicius, Wright, Royston,2

3

Figure 1 The network architecture. Five input units are fully connected to either ‘hemisphere’, and either hemisphere is fully connected to five output units. A hemisphere comprises 10 units and is fully recurrent. Two units from each hemisphere are used for inter-hemispheric connections; each of the two units in one hemisphere is connected to both units in the other hemisphere.

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Wisser, Huch, Huch & Zimmermann, 1999; Schwärzler,Bland, Holden, Campbell & Ville, 2004). The growthtrajectory for the networks modeling development inautism was derived from a meta-analysis of brain growthin children with autism (Redcay & Courchesne, 2005).Gompertz curves were fitted to these data to estimatethe prenatal trajectories (Luecke, Wosilait & Young,1995; Winsor, 1932; Wosilait, Luecke & Young, 1992).

As shown in Figure 2, network growth was discretized– i.e. the delay functions were approximated with stepfunctions. Copy units were added to or subtracted fromeach of the inter- and intra-hemispheric connections inaccord with the delay functions at the beginning of eachsimulated half-month. The network architecture wasthen held static for the duration of that simulated half-month. Training for 500 epochs constituted a simulatedhalf-month. As shown in Figure 2, as well, the inter-hemispheric connections were connected at 5 monthsbefore birth; this is approximately the timing of theestablishment of inter-hemispheric connections inprenatal development (Rakic & Yakovlev, 1968). Networktraining begins 5 months before birth as well.

The networks were trained to enumerate a set of inputstrings. The networks were provided with 32 input–output patterns, and were trained to associate each inputpattern with its corresponding output pattern. The inputpatterns were randomly generated binary strings. Theoutput patterns were the base 2 encodings of uniquenumbers assigned to the input patterns, duplicated forthe output units of either hemisphere, e.g. the output forpattern number 1 was 00001 00001. The input patternsfor both hemispheres together always corresponded to aunique output for all 32 input patterns. But, in order toexplore the potential impact of the different growthtrajectories on aspects of task performance that rely oninter-hemispheric communication and aspects that donot, half of the input–output pairs were unique withineither hemisphere, and half of the input patterns foreither hemisphere alone each corresponded to fourdifferent outputs. Thus, 16 of the input patterns could beassociated with their outputs without inter-hemisphericcommunication; and the other 16 were four-way ambigu-ous within either hemisphere, and so to generate thecorrect output, the network had to make use of theinter-hemispheric connections. Each of these 32 inputswas randomly assigned a number between 0 and 31, andpaired with the binary string comprising the five digitbase 2 encoding of that number concatenated with itself.Table 1 and Table 2 show the two sorts of input–outputpatterns. Examples were drawn randomly from suchtraining sets.

The networks were constructed and trained on LENS(Rhode, 1999) using the backpropagation of error algorithm

Figure 2 The growth trajectories of the networks modeling typically developing children and children with autism spectrum disorders. The head circumference growth trajectories are based on reported data. The inter-hemispheric conduction delay for the networks was a discretized function of age based on the head circumference growth trajectories. The delay function was:

DelayINTER(age, diagnosis) = * (HC(age, diagnosis)/π)/ConductionVelocity(age)

where HC(age, diagnosis) is the head circumference at the given age for the given diagnosis, and ConductionVelocity(age) is an increasing linear function of age. The delay associated with an intra-hemispheric connection was identical for both the networks modeling typical brain growth and the networks modeling autistic brain growth; the delay was of the inter-hemispheric delay associated with the model of typical brain growth.

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Table 1 Sixteen example input-target patterns which arefour-way ambiguous within each hemisphere. One half of oneof the training sets comprises these examples. The fourexamples which are bolded are identical with respect to theinputs to the left hemisphere. The corresponding inputs to theright hemisphere are, however, unique. The left and rightinputs together thus uniquely specify the outputs for bothhemispheres. Note that this same within-hemisphereambiguity exists for each of these 16 examples

Left hemisphere Right hemisphere

Input Target Input Target

1 0 0 0 1 → 0 0 0 0 1 0 1 0 0 0 → 0 0 0 0 10 1 0 0 0 → 0 1 1 1 0 0 0 1 0 0 → 0 1 1 1 01 1 1 1 0 → 1 0 0 0 1 1 0 1 0 1 → 1 0 0 0 11 0 0 0 1 → 0 1 0 1 1 1 0 1 0 1 → 0 1 0 1 11 1 0 1 1 → 1 0 0 1 1 0 0 1 0 0 → 1 0 0 1 11 1 1 1 0 → 1 0 1 1 0 0 1 0 0 0 → 1 0 1 1 00 1 0 0 0 → 1 0 1 1 1 1 0 1 0 1 → 1 0 1 1 11 1 1 1 0 → 1 1 0 0 1 0 0 0 0 0 → 1 1 0 0 11 1 0 1 1 → 1 1 0 1 0 0 1 0 0 0 → 1 1 0 1 01 0 0 0 1 → 0 1 0 0 0 0 0 1 0 0 → 0 1 0 0 01 1 0 1 1 → 1 1 1 0 0 1 0 1 0 1 → 1 1 1 0 00 1 0 0 0 → 1 1 1 0 1 0 1 0 0 0 → 1 1 1 0 11 0 0 0 1 → 0 1 0 0 1 0 0 0 0 0 → 0 1 0 0 10 1 0 0 0 → 1 1 1 1 1 0 0 0 0 0 → 1 1 1 1 11 1 1 1 0 → 0 0 1 0 0 0 0 1 0 0 → 0 0 1 0 01 1 0 1 1 → 0 0 1 1 0 0 0 0 0 0 → 0 0 1 1 0



(Rumelhart, Hinton & Williams, 1986) and gradientdescent with a learning rate of 0.01 and a momentumvalue of 0.9. A cross-entropy error function was used sothat the activation levels of the output units could beinterpreted as probabilities as well as confidence estimates.

To ensure the generality of the results, networks weretrained on 10 different training sets, and for each train-ing set were trained 20 times with different initial randomconnection weights. Additionally, the impact of the timebetween presentation of the input and evaluation of theresponse – i.e. the settling time – was assessed for eachtraining set and each weight initialization. Settling timeand conduction delay, together, determine how quickly,and for how long, the inter-hemispheric connections caninfluence the dynamics of the network, and so settlingtime was expected to have a strong influence on thedevelopment of functional and physical connectivity,and on performance. Each network was trained once witha short settling time, and once with a long settling time.The short settling time was 10 sweeps greater than the timerequired for activation to spread from one hemisphere tothe other in the networks following the brain growth tra-jectory of typically developing children. The long settlingtime was 20 sweeps greater than the short settling time.

Measures of connectivity and performance

The impact of the difference in the two growth trajecto-ries was analyzed for each network at multiple pointsduring training: at the simulated equivalent of birth,12, 24, 36, and 48 months of age. The impact on inter-hemispheric functional connectivity was measured. Theimpact on performance was measured. And the impact oninter-hemispheric physical connectivity was measured.

The functional analysis was done by removing all ofthe inter-hemispheric connections and measuring theimpact of these lesions on the network’s performance on

the training set. The measure of performance was thecross-entropy error. The difference between the pre- andpost-lesion cross-entropy error – i.e. the increase in errorcaused by the lesion – was calculated. This will be referredto as the lesion induced error. This measure was taken as anindication of the functional role of the inter-hemisphericconnections. A greater increase in the lesion inducederror was assumed to indicate a greater reliance on inter-hemispheric connections. This was assessed separatelyfor the two sorts of input patterns – the 16 binary stringsthat were unique within either hemisphere, and the 16 thatwere four-way ambiguous within either hemisphere.

The analysis of performance was done by measuringthe cross-entropy error for the intact network on thetraining set, and on a version of the training set in whichall targets were inverted. The network’s performance wastaken to be the percent correct, calculated as the errorproduced on the inverted version of the training set as apercentage of the total possible error. As with the func-tional measure, this was assessed separately for the twosorts of input patterns – the 16 binary strings that wereunique within either hemisphere, and the 16 that werefour-way ambiguous within either hemisphere.

The analysis of the impact of the difference in thegrowth trajectories on inter-hemispheric physical connectivitywas done by measuring connection weights. The analysisused the mean of the absolute value of the inter-hemisphericconnection weights – i.e. (Σi,j | wij |)/N, where wij is theweight associated with the link between the ith and jthunits, and the ith and jth units are in different hemispheres,and N is the number of such links – relative to the meanof the absolute value of the intra-hemispheric connectionweights. This gave a measure of the physical connectivityacross hemispheres relative to the physical connectivitywithin hemispheres.

To evaluate the effect of the growth trajectory on thesemeasures, four sorts of analyses were conducted: (i) theestimated marginal means were computed for bothgrowth conditions at each measured time-point; (ii) theestimated marginal means were compared between thetwo groups at each time-point; (iii) interactions betweengroup and age were computed for successive pairs oftime-points; and (iv) where the estimated marginal meansdecreased across time within a group, they were comparedto assess the reduction. To compare the estimatedmarginal means, for each time-point and settling time,repeated measures ANOVAs were done with group andtraining set as within-subject factors – the differentrandom initializations of a network being taken asdifferent subjects. To evaluate interactions between thetype of growth trajectory and age, for successive pairs ofthese time-points, repeated measures ANOVAs were donewith group, training set, and age as within-subject factors.And to assess the possibility of a reduction in functionalor physical connectivity, or a decline in performance,repeated measures ANOVAs were done for the group inquestion, for successive pairs of time-points, with trainingset, and age as within-subject factors.

Table 2 The other half of the training set shown in Table 1.In these examples, the inputs to each hemisphere uniquelyspecify the outputs

Left hemisphere Right hemisphere

Input Target Input Target

0 0 0 1 0 →→→→ 0 0 0 0 0 0 0 0 1 0 →→→→ 0 0 0 0 00 1 0 1 0 →→→→ 0 0 0 1 0 1 0 1 1 0 →→→→ 0 0 0 1 00 0 0 0 0 →→→→ 0 0 0 1 1 1 0 0 0 1 →→→→ 0 0 0 1 11 0 0 1 1 →→→→ 0 0 1 0 1 0 0 0 1 1 →→→→ 0 0 1 0 10 1 1 0 1 →→→→ 0 0 1 1 1 1 1 0 1 0 →→→→ 0 0 1 1 11 1 0 1 0 →→→→ 0 1 0 1 0 0 0 1 1 1 →→→→ 0 1 0 1 00 0 0 0 1 →→→→ 0 1 1 0 0 0 1 0 1 0 →→→→ 0 1 1 0 01 1 1 0 1 →→→→ 0 1 1 0 1 1 1 1 0 1 →→→→ 0 1 1 0 10 1 1 0 0 →→→→ 0 1 1 1 1 1 0 0 1 1 →→→→ 0 1 1 1 11 1 0 0 0 →→→→ 1 0 0 0 0 0 1 0 1 1 →→→→ 1 0 0 0 01 0 1 1 1 →→→→ 1 0 0 1 0 1 0 0 0 0 →→→→ 1 0 0 1 01 0 0 0 0 →→→→ 1 0 1 0 0 1 1 1 0 0 →→→→ 1 0 1 0 00 0 1 0 0 →→→→ 1 0 1 0 1 0 1 1 0 1 →→→→ 1 0 1 0 10 0 1 1 0 →→→→ 1 1 0 0 0 0 0 1 0 1 →→→→ 1 1 0 0 00 1 0 0 1 →→→→ 1 1 0 1 1 0 1 0 0 1 →→→→ 1 1 0 1 11 0 1 0 1 →→→→ 1 1 1 1 0 1 1 0 0 1 →→→→ 1 1 1 1 0



Results

The results of the analysis of the impact of removing theinter-hemispheric connections show an overall reductionin functional connectivity at approximately ‘24 months’in the networks that modeled autistic growth with shortsettling times, with considerable individual variation,and variation across training sets. The results of theanalysis of performance show a corresponding decline inperformance, with similar variability across individualsand training sets. And the results of the analysis of rela-tive inter-hemispheric weight show a parallel reductionin physical connectivity. The results of the functionalanalyses are presented in Figure 3 and Figure 4, and inTable 3 and Table 4; the results of the analysis of per-formance during learning are presented in Figure 5 andFigure 6, and in Table 5 and Table 6; and the results ofthe analyses of the relative inter-hemispheric connectionweight are presented in Figure 7 and Table 7.

Averaging over individual variation, and different out-comes for different training sets, the networks with shortsettling times grown at the rate of children with autismshowed a reduction in functional connectivity – in termsof the impact of removing the inter-hemispheric connec-tions – at approximately the simulated equivalent of24 months of age. These networks showed less impact ofthe lesions than their typically developing instantiationsat all measured time-points, but the difference wassmaller at ‘birth’ than at ‘12 months’, and much smallerat ‘12 months’ than thereafter. This is reflected in thedifferences in the estimated marginal means (Table 3 andTable 4), and in the fact that there were significantinteractions between group and age for these time-points

Table 3 The impact of removing the inter-hemispheric connections on the portion of the task which required inter-hemisphericcommunication. Three statistics are reported for both short and long settling times: (i) the estimated marginal means at each ofthe time-points; (ii) the main effect of group at each time-point; (iii) the interactions of group and age between successive pairs oftime-points. These statistics complement the results graphed in Figure 3

Birth 12 24 36 48

Short settling timei μASD 6.9 12.4 11.7 13.8 15.6

μTD 8.1 14.1 16.8 18.1 19.3

ii F(1, 19) 74.235 59.767 109.932 49.361 31.996p <0.001 <0.001 <0.001 <0.001 <0.001partial-η2 0.796 0.759 0.853 0.722 0.627

iii F(1, 19) 4.913 68.224 4.102 4.224p 0.039 <0.001 0.057 0.054partial-η2 0.205 0.782 0.178 0.182

Long settling timei μASD 10.6 15.3 17.7 19.3 20.3

μTD 10.7 15.1 17.5 17.9 19.1

ii F(1, 19) 0.175 0.178 0.138 15.778 11.190p 0.681 0.678 0.714 0.001 0.003partial-η2 0.009 0.009 0.007 0.454 0.371

iii F(1, 19) 1.283 0.012 22.790 1.434p 0.271 0.913 <0.001 0.246partial-η2 0.063 0.001 0.545 0.070

Figure 3 The impact of disconnecting the inter-hemispheric connections on the portion of the task which required inter-hemispheric communication. The left and right columns show the impact on the networks following the growth pattern in typical development and in autism, respectively. The top and bottom rows show the outcome for short and long settling times, respectively. Each curve represents the mean lesion induced error for a single training set.



(Table 3 and Table 4). This reduction occurred both forthe portion of the task which required inter-hemisphericcommunication, and for the portion that did not – thelatter presumably due to reorganization caused by theformer. And, as is evident from the estimated marginalmeans and the graphs of the mean lesion induced errorfor each training set (Figure 3 and Figure 4), the inter-action between group and age between ‘12 months’ and‘24 months’ indicates not just a decrease relative to thenetworks following the growth pattern in typical develop-ment, but an actual decrease in functional connectivity. Arepeated measures ANOVA on the lesion impact measuresfrom the networks grown at the rate of children withautism yielded a marginal main effect of age (F(1, 19)= 3.264, p = .087, partial η2 = 0.147) for the portion ofthe task that requires inter-hemispheric communication.But there was considerable variation in the timing of thereduction in functional connectivity. Adjusting for thelatency of this reduction by taking, for each network,either the period from ‘12 months’ to ‘24 months’, or ‘24months’ to ‘36 months’, whichever showed the greaterdecrease in functional connectivity, yielded a significantmain effect of age (F(1, 19) = 29.016, p < .001, partialη2 = 0.604). For the portion of the task that does notrequire inter-hemispheric communication, a repeatedmeasures ANOVA on the lesion impact measures fromthe networks grown at the rate of children with autismyielded a significant main effect of age for this timeperiod (F(1, 19) = 30.331, p < .001, partial η2 = 0.615).In both cases, however, there was substantial individualvariation, with some networks showing a continualincrease in functional connectivity, some showing aperiod of little change, and others showing substantialreductions. And, as is evident from the estimated

Figure 4 The impact of disconnecting the inter-hemispheric connections on the portion of the training set for which the inputs for either hemisphere uniquely specify the outputs for that hemisphere. The left and right columns show the impact on the networks following the growth pattern in typical development and in autism, respectively. The top and bottom rows show the outcome for short and long settling times, respectively. Each curve represents the mean lesion induced error for a single training set.

Table 4 The impact of removing the inter-hemispheric connections on the portion of the training sets comprising examples thatdo not require inter-hemispheric communication. Three statistics are reported for both short and long settling times: (i) the estimatedmarginal means at each of the time-points; (ii) the main effect of group at each time-point; (iii) the interactions of group and agebetween successive pairs of time-points. These statistics complement the results graphed in Figure 4

Birth 12 24 36 48


μTD 1.3 2.1 2.6 2.8 3.0

ii F(1, 19) 23.613 50.316 103.864 106.377 98.270p <0.001 <0.001 <0.001 <0.001 <0.001partial-η2 0.554 0.726 0.845 0.848 0.838

iii F(1, 19) 20.858 89.721 2.333 0.203p <0.001 <0.001 0.143 0.658partial-η2 0.523 0.825 0.109 0.011


μTD 1.4 1.9 2.1 2.2 2.3

ii F(1, 19) 3.851 1.560 0.033 <0.001 0.049p 0.065 0.227 0.858 0.989 0.827partial-η2 0.169 0.076 0.002 <0.001 0.003

iii F(1, 19) 0.027 3.269 0.397 0.407p 0.872 0.087 0.536 0.532partial-η2 0.001 0.154 0.022 0.022



marginal means for individual training sets (Figure 3and Figure 4), some training sets also resulted in continualincreases in functional connectivity overall, some in aperiod of little change, and others in reductions.

The networks with long settling times grown at therate of children with autism showed no such reductionin functional connectivity. Rather, these networksshowed greater functional connectivity at the simulatedequivalent of 36 and 48 months of age for the portion ofthe task that required inter-hemispheric communication(Table 3), though the effect was small. It is unclear whythis occurred, but perhaps it indicates that the longersettling times allowed the networks to compensate forthe increased conduction delay in the networks followingthe growth trajectory in autism – a difference that ismaximal between 16 and 32 simulated months of age,and is thus diminished at 36 and 48 simulated monthsof age.

The performance of the networks grown at the rate ofchildren with autism shows a similar pattern of develop-ment. On the portion of the task which required inter-hemispheric communication, averaging over individualvariation and different outcomes for different trainingsets, the networks with short settling times grown atthe rate of children with autism showed a fall-off inperformance – i.e. an increase in cross-entropy error – atapproximately the simulated equivalent of 24 months ofage (Figure 5 and Table 5). These networks, overall,performed worse on that portion of the task than theirtypically developing counterparts at all measured time-points, but the difference was smaller at ‘birth’ than at‘12 months’, and much smaller at ‘12 months’ thanthereafter. This is reflected in the differences in the esti-mated marginal means (Table 5), and in the fact that

Figure 5 The impact of the different patterns of growth on performance on the portion of the task which required inter-hemispheric communication. The left and right columns show the values for the networks following the growth pattern in typical development and in autism, respectively. The top and bottom rows show the outcome for short and long settling times, respectively. Each curve represents the mean performance for a single training set.

Table 5 Performance on the portion of the task which required inter-hemispheric communication. Three statistics are reportedfor both short and long settling times: (i) the estimated marginal means of the performance error at each of the time-points; (ii)the main effect of group at each time-point; (iii) the interactions of group and age between successive pairs of time-points. Thesestatistics complement the results graphed in Figure 5

Birth 12 24 36 48


μTD 73.2 79.6 81.4 82.2 82.8

ii F(1, 19) 9.060 21.364 193.165 101.767 67.116p 0.007 <0.001 <0.001 <0.001 <0.001partial-η2 0.323 0.529 0.910 0.843 0.779

iii F(1, 19) 0.556 181.463 18.721 35.910p 0.465 <0.001 <0.001 <0.001partial-η2 0.028 0.905 0.496 0.654


μTD 75.3 81.2 82.9 84.0 84.8

ii F(1, 19) 3.361 3.823 0.112 0.382 0.969p 0.082 0.065 0.741 0.544 0.337partial-η2 0.150 0.168 0.006 0.020 0.049

iii F(1, 19) 0.373 7.277 0.286 0.881p 0.548 0.014 0.599 0.360partial-η2 0.019 0.277 0.015 0.044



there was a significant interaction between group andage between ‘12 months’ and ‘24 months’ (F(1, 19) =181.463, p < .001, partial η2 = 0.905). As indicated bythe greater estimated marginal mean at ‘12 months’ thanat ‘24 months’, this is a decline in performance parallelingthe reduction in functional connectivity. Due to varia-tion in the timing of the decline in performance, a maineffect of age was not significant (F(1, 19) = 2.073, p <.166, partial η2 = 0.098). But adjusting for the latency ofthe decline by taking, for each network, either the periodfrom ‘12 months’ to ‘24 months’, or ‘24 months’ to‘36 months’, whichever showed the greater increase inperformance error, yielded a significant main effect ofage (F(1, 19) = 43.515, p < .001, partial η2 = 0.696).

As with functional connectivity, however, there wassubstantial individual variation, with some networksshowing a continual increase in performance, someshowing a period of little change, and others showingsubstantial declines in performance. And, as is evidentfrom the estimated marginal means for individualtraining sets (Figure 5), some training sets also resultedin continual improvement in performance, overall, somein a period of little change, and others in overall declinesin performance.

On the portion of the task which does not requireinter-hemispheric communication (Figure 6 and Table 6),the networks with short settling times grown at the rateof children with autism showed significantly inferior per-formance at ‘12 months’ (F(1, 19) = 36.465, p < .001,partial η2 = 0.657) and at ‘24 months’ (F(1, 19) = 54.152,p < .001, partial η2 = 0.740) in comparison to the net-works grown at the rate of typically developing children.But there was no actual decline in performance overtime. Rather, following this initial inferior performance,

Figure 6 The impact of the different patterns of growth on performance on the portion of the training set comprising examples for which the inputs for either hemisphere uniquely specify the outputs for that hemisphere. The left and right columns show the values for the networks following the growth pattern in typical development and in autism, respectively. The top and bottom rows show the outcome for short and long settling times, respectively. Each curve represents the mean performance for a single training set.

Table 6 Performance on the portion of the training sets comprising examples that do not require inter-hemispheric communication.Three statistics are reported for both short and long settling times: (i) the estimated marginal means of the performance error ateach of the time-points; (ii) the main effect of group at each time-point; (iii) the interactions of group and age between successivepairs of time-points. These statistics complement the results graphed in Figure 6

Birth 12 24 36 48


μTD 91.9 98.8 99.2 99.4 99.4

ii F(1, 19) 0.884 36.465 54.152 3.145 0.144p 0.359 <0.001 <0.001 0.092 0.709partial-η2 0.044 0.657 0.740 0.142 0.007

iii F(1, 19) 0.221 0.876 98.760 24.273p 0.644 0.361 <0.001 <0.001partial-η2 0.011 0.044 0.839 0.561


μTD 91.5 98.1 98.6 98.9 99.0

ii F(1, 19) 1.208 2.477 0.121 0.963 0.289p 0.285 0.132 0.732 0.339 0.597partial-η2 0.060 0.115 0.006 0.048 0.015

iii F(1, 19) 1.027 8.124 5.59 2.519p 0.324 0.010 0.029 0.129partial-η2 0.051 0.300 0.227 0.117



the performance of the networks grown at the rate ofchildren with autism improved rapidly, and by ‘48months’, was comparable to the performance of the net-works grown at the rate of typically developing children.

The networks with long settling times grown at therate of children with autism showed no such fall-off inperformance, neither for the portion of the task thatrequired inter-hemispheric interaction (Figure 5 andTable 5), nor for the portion of the task that did not(Figure 6 and Table 6).

This pattern of development of functional connectivity,and of performance, is directly reflected in the patternsof development of physical connectivity as measured byrelative inter-hemispheric connection weight (Figure 7and Table 7). Averaging over individual variation, anddifferent outcomes for different training sets, the networkswith short settling times grown at the rate of childrenwith autism showed a reduction in physical connectivityat approximately the simulated equivalent of 24 monthsof age. These networks, overall, had reduced relativeinter-hemispheric connection weights at all measuredtime-points, but the difference increases substantially at‘12 months’. This is reflected in the differences in theestimated marginal means (Table 7), and in the fact thatthere was a significant interaction between group andage between ‘12 months’ and ‘24 months’ (Table 7).And, as with the pattern of development of functionalconnectivity, and of performance, the interaction betweengroup and age between ‘12 months’ and ‘24 months’indicates not just a decrease relative to the networksfollowing the growth pattern in typical development, butan actual reduction in physical connectivity. A repeatedmeasures ANOVA on the relative inter-hemisphericweight measures from the networks trained with shortsettling times and grown at the rate of children with autism

Figure 7 The mean inter-hemispheric connection weight as a percentage of the mean intra-hemispheric connection weight. The left and right columns show the values for the networks following the growth pattern in typical development and in autism, respectively. The top and bottom rows show the outcome for short and long settling times, respectively. Each curve represents the mean relative inter-hemispheric weight for a single training set.

Table 7 Relative inter-hemispheric connection weight. Three statistics are reported for both short and long settling times: (i) theestimated marginal means at each of the time-points; (ii) the main effect of group at each time-point; (iii) the interactions of groupand age between successive pairs of time-points. These statistics complement the results graphed in Figure 7

Birth 12 24 36 48


μTD 255.5 353.3 394.9 422.1 442.2

ii F(1, 19) 91.287 40.725 203.527 272.155 182.560p <0.001 <0.001 <0.001 <0.001 <0.001partial-η2 0.828 0.682 0.915 0.935 0.906

iii F(1, 19) 2.758 690.058 302.471 132.939p 0.133 <0.001 <0.001 <0.001partial-η2 0.127 0.973 0.941 0.875


μTD 225.7 251.2 262.9 270.9 277.3

ii F(1, 19) 0.624 0.635 2.118 3.748 4.388p 0.439 0.435 0.162 0.068 0.050partial-η2 0.032 0.032 0.100 0.165 0.188

iii F(1, 19) 3.539 2.653 4.447 1.544p 0.075 0.120 0.048 0.229partial-η2 0.157 0.123 0.190 0.075



yielded a significant main effect of age for this timeperiod (F(1, 19) = 68.470, p < .001, partial η2 = 0.783).

As with functional connectivity and performance,however, there was substantial individual variation, withsome networks showing a continual increase in physicalconnectivity, some showing a period of little change, andothers showing reductions. As is evident from theestimated marginal means for individual training sets(Figure 7), however, the input did not have the same sortof influence on physical connectivity as it did onperformance and functional connectivity. This mayindicate that there was reorganization in all cases, butthat some training sets posed greater problems forthis process than others, and so the physical changesresulted in better functional recovery in some cases thanin others.

The networks with long settling times grown at therate of children with autism showed no such reductionin physical connectivity. Rather, similar to the pattern ofdevelopment in functional connectivity, these networksshowed a small increase in physical connectivity at 48simulated months of age (Table 7). This increase inrelative inter-hemispheric weight reflects only an increasein the inter-hemispheric weights; the mean intra-hemispheric weights are virtually identical to the networksfollowing the typical growth trajectory. Again, it isunclear why this occurred, but perhaps the longersettling times allowed the networks to compensate forthe increased conduction delay in the networks followingthe growth trajectory in autism.

Discussion

Autism is a developmental disorder defined by impair-ments in reciprocal social interactions, impairments inverbal and nonverbal communication, and a restrictedrepertoire of activities and interests (American PsychiatricAssociation, 1994). In addition to these core symptoms,however, there are usually deficits in multiple otherareas, e.g. imitation (Aldridge, Stone, Sweeney & Bower,2000; Charman, Swettenham, Baron-Cohen, Cox, Baird& Drew, 1997; DeMyer, Alpern, Barton, DeMeyer,Churchill, Hingtgen, Bryson, Pontius & Kimberlin,1972; Hobson & Lee, 1999; V. Jones & Prior, 1985;Rogers, Bennetto, McEvoy & Pennington, 1996; Royeurs,Van Oost & Bothuyne, 1998; Sigman & Ungerer, 1984;Smith & Bryson, 1998; Stone, Lemanek, Fishel, Fernandez& Altemeier, 1990; Stone, Ousley & Littleford, 1997),motor coordination (Dawson, Osterling, Meltzoff &Kuhl, 2000; Kanner, 1943; Teitelbaum, Teitelbaum, Nye,Fryman & Maurer, 1998), perception of rapid auditorytransitions (Oram Cardy, Flagg, Roberts, Brian & Roberts,2005), and of visual motion (Bertone, Mottron, Jelenic &Faubert, 2003; Gepner & Mestre, 2002; Gepner, Mestre,Masson & de Schonen, 1995; Milne, Swettenham, Hansen,Campbell, Jeffries & Plaisted, 2002; Spencer, O’Brien,Riggs, Braddick, Atkinson & Wattam-Bell, 2000). There

are also areas of strength, e.g. discrimination anddetection of simple perceptual patterns, and analysis ofvisuospatial details (Bonnel, Mottron, Peretz, Trudel,Gallun & Bonnel, 2003; Happé, 1999; Jolliffe & Baron-Cohen, 1997; O’Riordan, Plaisted, Driver & Baron-Cohen,2001; Plaisted, O’Riordan & Baron-Cohen, 1998; Shah& Frith, 1983). But autism is heterogeneous in its pres-entation – six of the 12 aspects of the three core symptomssuffice for a diagnosis of autism, so individuals presentwith different sets of behaviors. There is also substantialvariation in terms of the subsets of non-core deficits thatare present and strengths that are present. And individualsshow differing degrees of superiority in their strengths,and differing degrees of severity in both core and non-core deficits. Additionally, the onset of the disorder varies:some children exhibit a failure to progress appropriatelyand show gradual development of any aberrant behaviors;others appear to develop normally for one or two yearsand then show sudden losses in acquired behaviors andthe appearance of aberrant behaviors (Bailey, Phillips &Rutter, 1996; Filipek, Accardo, Baranek, Cook, Dawson,Gordon, Gravel, Johnson, Kallen, Levy, Minshew, Prizant,Rapin, Rogers, Stone, Teplin, Tuchman & Volkmar, 1999;Kolvin, 1971; Lainhart, Ozonoff, Coon, Krasny, Dinh,Nice & McMahon, 2002; Luyster, Richler, Risi, Hsu,Dawson, Bernier, Dunn, Hepburn, Hyman, McMahon,Nice-Goudie, Minshew, Rogers, Sigman, Spence, Goldberg,Tager-Flusberg, Volkmar & Lord, 2005; Short & Schopler,1988; Siperstein & Volkmar, 2004).

Associated with this behavioral profile are findings ofincreased head and brain size (Aylward et al., 2002;Bailey et al., 1993; Bailey et al., 1998; Bauman & Kemper,1985; Courchesne et al., 2003; Courchesne et al., 2001;Davidovitch et al., 1996; Dementieva et al., 2005;Fombonne et al., 1999; Hazlett et al., 2005; Hultmanet al., 2002; Kemper & Bauman, 1998; Lainhart et al.,1997; Miles et al., 2000; Piven et al., 1995; Redcay &Courchesne, 2005; Sparks et al., 2002; Waiter et al.,2004; Woodhouse et al., 1996), and reduced large-scalefunctional connectivity (Castelli et al., 2002; Just et al.,2004; Kana et al., 2006; Koshino et al., 2005; Ring et al.,1999) and structural connectivity (Chung, Dalton,Alexander & Davidson, 2004; Egaas et al., 1995; Lewis& Courchesne, 2004; Lewis et al., 2003, 2004; Maneset al., 1999; Piven et al., 1997; Vidal et al., 2006; Waiteret al., 2005).

The modeling results presented here suggest that theabnormal brain growth trajectory in autism, via theinfluence of conduction delay, may provide an explanationfor the findings of reduced large-scale functional andstructural connectivity, and perhaps even for severalaspects of the behavioral phenotype.

The decline in inter-hemispheric functional connectivityseen in the models with short settling times grown at therate of children with autism provides almost directly forthe findings of reduced large-scale functional connectivityin autism (Castelli et al., 2002; Just et al., 2004; Kanaet al., 2006; Koshino et al., 2005; Ring et al., 1999). These



reductions have been found in language tasks (Just et al.,2004; Kana et al., 2006), visual motion processing tasks(Castelli et al., 2002), and tasks involving workingmemory (Koshino et al., 2005). Language requires veryrapid integration of prosodic and syntactic informationin the acoustic signal, and possibly also the dynamicvisual information in the face and in gesture. Workingmemory appears to rely on verbal rehearsal (Baddeley& Hitch, 1974). And motion processing utilizes delaycircuits, which are inherently dependent on temporalprecision. These temporal processing demands for lan-guage and motion processing tasks make it reasonable tospeak of such networks as having short settling times.There are, however, no longitudinal data on functionalconnectivity in children with autism, or even cross-sectional data.

The decline in inter-hemispheric physical connectivityseen in the models with short settling times grown at therate of children with autism, similarly, provides almostdirectly for the findings of reduced large-scale structuralconnectivity in autism (Chung et al., 2004; Egaas et al.,1995; Lewis & Courchesne, 2004; Lewis et al., 2003,2004; Manes et al., 1999; Piven et al., 1997; Vidal et al.,2006; Waiter et al., 2005). Cross-sectional and longitudinaldata indicate that this is a reduction that occursdevelopmentally (Lewis & Courchesne, 2004; Lewiset al., 2004), and is related to brain-size (Lewis &Courchesne, 2004; Lewis et al., 2004). But the function-ality of the networks involved, and their temporaldemands, must be inferred from the correspondencewith the findings of functional reductions.

The fall-off of functional and physical connectivityseen in some of the models with short settling timesgrown at the rate of children with autism indicates thatthe brain growth trajectory in autism may result in aninitial near-normal commitment to representations involv-ing long-distance connections, followed by substantialreorganization that abandons these large-scale networksin favor of functionally localized representations. Thisprocess of reorganization is plausibly extremely func-tionally disruptive, and as suggested by the increase inperformance error seen in these models, might be expectedto have negative behavioral consequences. The modelingresults indicate that, via such a process of reorganization,the brain overgrowth in autism may explain a number ofaspects of the phenotype: the timing of the onset of thebehavioral symptoms, the possibility of regression, thesorts of behaviors that are affected, and the heterogeneity.

Autism is generally reported to have a gradual onsetwith subtle signs presenting over the first year, and moreobvious behavioral symptoms usually appearing late inthe second year, or early in the third (Lord, Rutter,Goode, Heemsbergen, Jordan, Mawhood & Schopler,1989; Volkmar, Stier & Cohen, 1985). But children laterdiagnosed with autism may, until around 18 to 30months, develop normally or with subtle abnormalities,and then simply fail to progress, or may even regress –i.e. lose skills that they had already acquired (Davidovitch,

Glick, Holtzman, Tirosh & Safir, 2000; Fombonne &Chakrabarti, 2001; Goldberg, Osann, Filipek, Laulhere,Jarvis, Modahl, Flodman & Spence, 2003; Kurita, 1985;Lainhart et al., 2002; Lord, Shulman & DiLavore, 2004;Luyster et al., 2005; Rapin & Katzman, 1998; Rogers,2004; Rutter & Lord, 1987; Shinnar, Rapin, Arnold,Tuchman, Shulman, Ballaban-Gil, Maw, Deuel &Volkmar, 2001; Simons & Oishi, 1987; Wilson, Djukic,Shinnar, Dharmani & Rapin, 2003). Both patterns ofdevelopment thus show a decline in performance duringthe latter part of the second year, or early in the third.At all simulated ages, the networks with short settlingtimes grown at the rate of children with autism showeda reduction in performance in comparison to their typic-ally developing counterparts. This difference, however,became much greater between 12 and 24 simulated monthsof age, or in some cases, between 24 and 36 simulatedmonths of age. The correspondence, in terms of the ageat which performance is most affected, between the model-ing results and the patterns of development in autismsuggests that the brain overgrowth in autism may forcereorganization, and thereby bring about the appearanceof the behavioral symptoms. In the models following thegrowth trajectory in autism, inter-hemispheric conductiondelay is maximal between 16 and 32 months.

Regression occurs in 20% to 50% of children withautism, and is characterized by a significant loss of lan-guage and nonverbal communication skills (Davidovitchet al., 2000; Goldberg et al., 2003; Kurita, 1985; Rapin& Katzman, 1998; Rutter & Lord, 1987; Tuchman,Rapin & Shinnar, 1991). Many of these children showsignificant cognitive impairments, and many becomenonverbal (Volkmar & Cohen, 1989; Wilson et al., 2003).There is generally gradual abatement of behavioralabnormalities in autism (DeMyer, Barton, DeMeyer,Norton, Allen & Steele, 1973; Gillberg, 1991; Kanner,1943; Kobayashi, Murata & Yoshinaga, 1992; Lotter,1978; Wolf & Goldberg, 1986), but the prognosis seemsto be at least partially determined by the severity of theearly symptoms (Coplan & Jawad, 2005). Children withlate onset autism with regression generally show limitedrecovery (Volkmar & Cohen, 1989; Wilson et al., 2003).The modeling results suggest that cases of autism withregression may have the same etiology as cases of autismin which there is a failure to progress, or in which theonset is more gradual – i.e. the reorganization is drivenby brain overgrowth. The reduction in performance ataround 24 simulated months of age for the networksgrown at the rate of children with autism was, in somecases, just a reduction relative to the typically developingnetworks; on average, there was a slight decline inperformance – perhaps akin to a failure to progress inautism; and in some cases, this decline was substantial.Some of the networks showed a fall-off in performanceof almost 10% – or, in terms of performance abovechance, a decline of almost 25%. And this decline inperformance would most likely be substantially larger ifthe networks followed the more extreme growth trajectory



of some children with autism; and the impact on per-formance would most likely be larger still if the trainingsets increased in complexity over time – more in keepingwith, for example, the problem of language acquisition.With a more extreme growth trajectory and more com-plex input, the number of networks showing suchdeclines would also probably increase. A lesser degreeof recovery would probably be seen as well, though real-istic recovery results would probably, at a minimum,require the models to become less plastic over time, andto include pruning; the models used here have the samecapacity to learn at all points in development, andpermit weights to be reduced to zero, and then becomenon-zero again.

The characteristic loss of language and communicationskills in cases of autism with regression may be in partdue to the complexity of the input for those particulartasks, but the modeling results suggest that the rapidtemporal demands of tasks such as these, and theirreliance on inter-hemispheric connectivity, will makethem particularly likely to be affected. As suggested bythe far smaller impact on functional and physical con-nectivity, and on performance, for the models with longsettling times, or for the portion of the task for whichinter-hemispheric communication was not necessary, theconsequences of the growth trajectory depend on thenature of the task. Networks should be expected to benegatively affected to the extent that those networksmust rapidly integrate their inputs, to the extent thatthose networks comprise connections with substantiallydifferent conduction delays, and to the extent that therapidity of the brain growth outpaces the ability of thesystem to compensate for the changes. The failure ofsuch networks may underlie many of the behavioraldeficits in autism, either directly or indirectly – indirectlyin that behaviors that rely developmentally on the func-tioning of affected circuits cannot be expected to developnormally. Some of the core behavioral symptoms ofautism, as well as many of the other associated abnor-malities, may simply reflect network disruptions causedby unequal changes in conduction delay as a result ofrapid changes in brain size.

Language abilities, for example, rely on the rapidintegration of syntactic and prosodic information in theacoustic signal, as well as the information available infacial dynamics and gesture. These networks span thebrain. And the long-distance interactions may be parti-cularly important in language acquisition. Languageacquisition appears to make substantially greater use oflong-distance connections than does the adult system.Language acquisition, for instance, appears to rely onprosodic cues to a much greater extent than does adultlanguage processing (Gerken, 1996; Hirsh-Pasek, KemlerNelson, Jusczyk, Cassidy, Druss & Kennedy, 1987), andso on the interactions between the hemispheres. Studiesof language processing show more bi-lateral activationin infants than in adults (Dehaene-Lambertz, 2000;Dehaene-Lambertz & Dehaene, 1994; Dehaene-

Lambertz, Dehaene & Hertz-Pannier, 2002; Sachs &Gaillard, 2003). Moreover, disruptions in the networksresponsible for processing any of the linguistic, andsupra-linguistic, input – e.g. the networks responsible forlow-level auditory or visual processing, for integration oflow-level information, or for processing at more abstractlevels – may contribute to a language deficit.

The networks that underlie auditory speech percep-tion extend from the cochlea to the brain stem to ante-rior and posterior regions of the temporal cortex (Belin,Zatorre, LaFaille, Ahad & Pike, 2000; Binder, Frost,Hammeke, Bellgowan, Springer, Kaufman & Possing,2000; Wise, Scott, Blank, Mummery, Murphy & War-burton, 2001), prefrontal areas (Fiez, Tallal, Raichle,Miezin, Katz & Petersen, 1995; Schubotz & von Cramon,2001), the cerebellum (Hazeltine, Grafton & Ivry, 1997;Ivry & Keele, 1989), and the basal ganglia (Meck &Benson, 2002; Rammsayer & Classen, 1997). The rapidtemporal processing demands of speech (Benasich,Thomas, Choudhury & Leppänen, 2002) place highdemands on such a widely distributed system. Thusauditory speech perception should be expected to beimpacted by the early brain overgrowth in autism.Results from EEG studies of auditory brain stemresponses to acoustic stimuli indicate that there areincreased conduction times from the cochlear nerve tothe contralateral lateral lemniscus and inferior colliculusin individuals with autism (Maziade, Merette, Cayer,Roy, Szatmari, Cote & Thivierge, 2000; Rosenhall,Nordin, Brantberg & Gillberg, 2003; Wong & Wong,1991); and delayed cortical responses to sinusoidal toneshave been found in MEG studies (Gage, Siegel &Roberts, 2003). The question of whether or not theseabnormalities translate into deficits in acoustic speechperception in autism is largely unaddressed, but deficitsin rapid temporal processing have been reported (OramCardy et al., 2005), and tone and phoneme changes havebeen found to evoke a delayed cortical response comparedto normal controls (Kasai, Hashimoto, Kawakubo,Yumoto, Kamio, Itoh, Koshida, Iwanami, Nakagome,Fukuda, Yamasue, Yamada, Abe, Aoki & Kato, 2005),with a significant positive relation between this latencydelay and symptom severity. The ability to process briefacoustic transitions is critical for speech perception, andsuch impairments in this ability during development arelikely to interfere with language acquisition. And deficitselsewhere may also interfere.

Visual and auditory integration is also likely to beimportant in early language acquisition. In typicallydeveloping children, and in adults, pairing visuallypresented speech – i.e. an image sequence of a face thatis mouthing words – with noisy auditory stimuli resultsin improved perceptual accuracy in comparison toperformance on either modality alone (Calvert, Brammer& Iversen, 1998; Massaro, 1998; Summerfield & McGrath,1984). And visually presented speech has been found toactivate both visual cortex and auditory cortex (Calvert,Bullmore, Brammer, Campbell, Williams, McGuire,



Woodruff, Iversen & David, 1997; Calvert & Campbell,2003; Campbell, MacSweeney, Surguladze, Calvert,McGuire, Suckling, Brammer & David, 2001; MacSweeney,Amaro, Calvert, Campbell, David, McGuire, Williams,Woll & Brammer, 2000; Pekkola, Ojanen, Autti,Jääskeläinen, Möttönen, Tarkiainen & Sams, 2005;Santi, Servos, Vatikiotis-Bateson, Kuratate & Munhall,2003). But this integration relies on long-distanceconnections, and must occur rapidly, and so is likely tobe impacted by the brain overgrowth in autism. Childrenwith autism show the expected effect: they show a muchsmaller influence of visually presented speech on theirperformance in identifying noisy auditory stimuli(Massaro, 1987; Massaro & Bosseler, 2003). And visualspeech processing may be particularly important forlanguage acquisition in the context of impairments inspeech-related auditory processing abilities.

The integration of visual and auditory information,moreover, involves the amygdala (E.G. Jones & Powell,1970; Turner, Mishhkin & Knapp, 1980; Webster, Unger-leider & Bachevalier, 1991), which has been reported as apossible neural basis of the affect deficits in autism(Aylward, Minshew, Goldstein, Honeycutt, Augustine,Yates, Barta & Pearlson, 1999; Baron-Cohen, Ring,Bullmore, Wheelwright, Ashwin & Williams, 2000;Bauman & Kemper, 1985; Schumann, Hamstra, Goodlin-Jones, Lotspeich, Kwon, Buonocore, Lammers, Reiss &Amaral, 2004).

The processing of visually presented speech also relieson visual motion processing, which should also beexpected to be negatively impacted by the early brainovergrowth in autism. The visual system extends fromthe retina to the lateral geniculate nucleus to striatecortex, and then to higher-level processing areas inoccipital, parietal, and temporal cortex, and to frontalcortex and numerous subcortical areas (Van Essen &Gallant, 1994). Delay circuits are at the core of visualmotion processing networks, and at multiple levels ofprocessing the precisely timed activation of pools ofneurons is critical. These delay circuits calculate thedifference in the timing of the activation of the receptivefields corresponding to two different spatial locations onthe retina. Uneven alterations to the conduction delaysof the axons that comprise such delay circuits will alterthe motion that is detected and the delay with which thedetector fires. So the pools of neurons that detect anygiven motion will be negatively affected in two ways.And the neurons that integrate the outputs of these delaycircuits will be similarly vulnerable. The early brainovergrowth in autism should thus be expected to impactvisual motion perception, and the effect should be greaterfor faster motion and complex patterns. Children withautism are reported to be less sensitive to visual full-fieldradiating flow fields than typically developing children(Gepner et al., 1995), and the deficit is reported toincrease with speed (Gepner & Mestre, 2002). Andchildren with autism are reported to have significantlyhigher motion coherence thresholds with global motion

stimuli (Spencer et al., 2000), random dot kinemato-grams (Milne et al., 2002) and texture-defined motionstimuli (Bertone et al., 2003) than typically developingchildren, but not for luminance-defined motion stimuli(Bertone et al., 2003).

Visual motion processing is, moreover, required toprocess social cues such as dynamic emotional expres-sions, eye gaze shifts, and gesture. Children with autismare reported to perform significantly worse than typicallydeveloping children on tasks involving the processing offacial dynamics, such as emotional expressions andmovements of the lips and eyes (Gepner, Deruelle &Grynfeltt, 2001). And this performance difference isreported to be substantially reduced when the stimuli aredisplayed more slowly (Gepner et al., 2001).

Deficits in motion processing should also be expectedto impact an individual’s ability to learn about, andrespond to, the dynamic properties of the environment.Motor skills show the expected effect: in the firstdescription of autism, Kanner (1943) described childrenwith autism as ‘clumsy in gait and gross motor perform-ances’; and subsequent research has established thatmotor deficits are, perhaps reliably, present in childrenwith autism (Dawson et al., 2000; Teitelbaum et al., 1998).

And deficits in motion processing should also beexpected to impair an individual’s ability to perceive theactions of others. Autistic children are reported to beimpaired in the perception of biological motion presentedas point-light animations (Blake, Turner, Smoski, Pozdol& Stone, 2003). This deficit might in turn be expected tolead to an impaired ability to learn motor behaviorswhich are modeled by others.

Additionally, the long-distance connections that linkvisual cortex with pre-motor cortex – the mirror neuronsystem (di Pellegrino, Fadiga, Fogassi, Gallese &Rizzolatti, 1992; Rizzolatti, Fadiga, Gallese & Fogassi,1996) – should be negatively affected by the early brainovergrowth in autism. Neurons in premotor cortex thatdischarge when executing an action also discharge whenobserving that action (di Pellegrino et al., 1992; Riz-zolatti et al., 1996; Rizzolatti, Fogassi & Gallese, 2001).The ability to carry out such internal simulation mayplay a critical role in the ability to understand otherindividuals’ movements, and the ability to understandsocial interactions (Rizzolatti & Craighero, 2004;Williams, Whiten & Singh, 2004). Thus imitation, andimitation learning, should be negatively affected inautism. Individuals with autism spectrum disorders havebeen reported to lack a mu rhythm response when observ-ing another performing an action (Oberman, Hubbard,McCleery, Altschuler, Ramachandran & Pineda, 2005)– carrying the implication of a dysfunctional mirrorneuron system. Imitation ability in autism is wellresearched, and support for a deficit in autism isunequivocal. Toddlers with autism have been found tohave a deficit in meaningful and non-meaningful actionimitation compared to typically developing toddlers(Charman et al., 1997; Stone et al., 1997). Young



children with autism show clear deficits on body andmotor-object imitation tasks (DeMyer et al., 1972), onsimple imitation tasks from the Motor Imitation Scale(Sigman & Ungerer, 1984), on motor imitation tasks (V.Jones & Prior, 1985), on imitative ‘pretend’ actions andbody movements (Stone et al., 1990), and on gestural(Aldridge et al., 2000; Royeurs et al., 1998) and proceduralimitation (Royeurs et al., 1998). And adolescentscontinue to show deficits in symbolic and non-symbolicimitation (Rogers et al., 1996; Smith & Bryson, 1998),pantomime tasks (Rogers et al., 1996), and the imitationof the style in which an action is performed (Hobson &Lee, 1999).

Disruptions to networks such as these, which operateat a relatively low level, may also interfere with higher-level processing. And as suggested by the modelingresults, the reorganization required for one task mayhave negative consequences for others. But this reorgan-ization may also underlie some of the areas of strengthseen in autism. Individuals with autism perform well onvisual search tasks (O’Riordan et al., 2001; Plaistedet al., 1998), the block design and object assembly subtestsof the Wechsler Intelligence Scale (Frith, 1989; Shah &Frith, 1983), the embedded figures task of the Wechslerintelligence test (Jolliffe & Baron-Cohen, 1997; Mitchell& Ropar, 2004; Shah & Frith, 1983), perceptual learningtasks (Plaisted et al., 1998), and global precedence tasks(Plaisted, Swettenham & Rees, 1999). Individuals withautism appear to employ a cognitive strategy for suchtasks which relies more heavily on low-level processesimplemented in relatively local circuits (Koshino et al.,2005; Ring et al., 1999). In the embedded figures task –a task requiring detection and discrimination of simplestimuli, and analysis and memory of perceptual detail –fMRI results show less extensive activation overall inindividuals with autism compared to normal controls,no activation of prefrontal areas normally related tomemory, and more activation in visual cortex (Ringet al., 1999). Visual cortex, in fact, appears to play agreater role than normal in satisfying the memoryrequirements of such tasks (Koshino et al., 2005). In ann-back task, individuals with autism were found toactivate visual cortex to a greater extent than normalcontrols (Koshino et al., 2005). And measures offunctional connectivity from fMRI indicate that thisaltered pattern of activation involves relatively small-scale networks (Castelli et al., 2002; Just et al., 2004;Koshino et al., 2005; Ring et al., 1999). For tasks inwhich high-level processing normally interferes withlow-level processing – e.g. the global precedence task,the embedded figures task, and the block design task –the reduced influence of high-level processing on low-levelprocessing should logically result in superior performance.And in the block design task, for instance, children withautism show superior performance only when thedesigns are presented whole, but not when the designsare presented as segmented pieces (Shah & Frith, 1993).The Gestalt design appears to have less impact on children

with autism than on typically developing children. Thishas been taken as support for the theory of weak centralcoherence (Shah & Frith, 1993); the hypothesis presentedhere can be seen, for these cases, as providing a mecha-nism which explains why children with autism exhibitweak central coherence.

This mechanism, and the modeling results presentedabove, also provide an explanation for the heterogeneityin autism. The developmental performance measures forthe networks grown at the rate of children with autismshowed considerable between-subject variability in boththe degree to which their performance was reducedrelative to the networks grown at the rate of typicallydeveloping children, and the time at which the greatestreduction occurred. There was also considerable variabilitybetween training sets. The individual variation suggeststhat the precise impact of the brain growth trajectory onfunctional connectivity, behavior, and physical connec-tivity is likely to depend on potentially small differencesin brain structure. The variation for different trainingsets indicates that this relationship is also likely to bemodulated by differences in the environment. And thesesources of variability can affect the networks subservingdifferent functions relatively independently. Thus thesame growth trajectory can impact different subsets ofbehaviors differentially in different individuals. Addi-tionally, variability in brain size prenatally, and early inpostnatal development, should lead to differences in thedegree of commitment to widely distributed networks,and therefore in the amount of functional disruptionthat later rapid brain growth would produce. Variabilityin the amount of brain development that occurs beforethe period of accelerated brain growth should have asimilar impact, and will also interact with developmentalchanges in neuroplasticity. And more rapid brain growthis more likely to be disruptive, as are differences in maxi-mum brain size achieved.

Core aspects of the behavioral phenotype in autismspectrum disorders, as well as many of the ostensiblyperipheral aspects, may thus be related to the effect thatabnormalities in the growth trajectory have on conductiondelay and, in turn, functional and physical connectivityand performance. The modeling results presented heretake this beyond pure speculation; they provide an in-principle demonstration. The different outcomes forthe two growth patterns reflect differences solely ininter-hemispheric conduction delay. But these models,and the input–output pairs they were trained on, areobviously very far from reality. The results are thussimply suggestive with respect to autism; and the abovespeculations are merely an initial exploration of theaspects of autism that might, via this mechanism, berelated to the early brain overgrowth. But the relationsbetween the trajectory of brain growth and functionalconnectivity, the behavioral phenotype, and physicalconnectivity, are almost unknown; and the empiricalresearch that tests the hypothesis outlined here, for themost part, remains to be done.



Acknowledgement

This research was supported by grant NIH/NIMHR01-MH60517 to the second author.

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Received: 16 November 2005Accepted: 17 January 2007

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